4. Working in batches, strain stew through large sieve into second large pot, reserving solids. Set food mill over second pot. Working with 2 cups reserved stew-base solids at a time, press through food mill to extract remaining broth and some fish and vegetables to make 13 cups stew base. Discard remaining solids.
Boil stew base until reduced to 10 cups, stirring occasionally, about 15 minutes. (Can be made 1 day ahead. Chill stew base uncovered until cold, then cover and keep chilled. Keep lobster and shrimp chilled.)

Finish Stew:

1. Bring stew base to simmer; keep warm. Combine scallops, crabmeat (if desired), shrimp, and lobster meat in large bowl. Add flour; toss gently to coat. Place seafood in sieve; shake off excess flour. Heat 3 tablespoons oil in heavy large skillet over medium-high heat. Add half of seafood. Sauté 1 minute. Add half of butter, then 2 tablespoons parsley, half of garlic, and half of shallot. Sauté until scallops and shrimp are just opaque in center and all seafood is beginning to brown, about 4 minutes. Transfer to large bowl. Repeat with remaining oil, butter, seafood, 2 tablespoons parsley, garlic, and shallot; transfer to same bowl. Add wine to skillet and boil until reduced to glaze, scraping up browned bits, about 3 minutes. Mix glaze into seafood.